Slip-discreteness-corrected strain gradient crystal plasticity (SDC-SGCP) theory

A thin aluminium sheet comprising of large polycrystals is pulled in uniaxial tension and the resulting surface profile is measured in a scanning electron microscope. The surface profile near the grain boundaries reveals a local deformation pattern of width of a few micrometres and is strong evidence for strain gradient effects. Numerical analyses of a bicrystal undergoing in-plane tensile deformation are also studied using a strain gradient crystal plasticity theory and also by using a strain gradient plasticity theory for an isotropic solid. Both theories include an internal material length scale. An interfacial potential that penalizes the dislocations in crossing the grain boundary is included in the analysis. The results indicate that the surface profile is strongly dependent upon the choice of this potential and on the material length scale.

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

Implicit iterative finite element scheme for a strain gradient crystal plasticity model based on self-energy of geometrically necessary dislocations

Mechanism-based strain gradient crystal plasticity—I. Theory

An evaluation of higher-order single crystal strength models for constrained thin films subjected to simple shear

The anisotropy of single crystal copper and crystal orientation have a significant effect on the micro-milling process. At present, there is no systematic and perfect theory to explain the influence of single crystal orientation on the micro-milling process. Therefore, it is urgent to conduct an in-depth study on the micro-milling process of single crystal copper. In this paper, based on the theory of crystal plasticity, considering the anisotropy of single crystal copper, the VUMAT material subroutine of single crystal copper is programmed by the Fortran language, and the crystal plastic constitution is introduced into the finite element simulation. The model of the micro-milling tool and work-piece is established and meshed. Considering the friction among the tool and the work-piece, material removal, etc., the three-dimensional finite element simulation model of single crystal copper micro-milling process is achieved by ABAQUS software. The validity of the simulation model of the micro-milling process of single crystal copper considering the single crystal plastic constitution is verified by experimental micro-milling forces. The research has explored a feasible way to predict the micro-milling force of single crystal copper, and has provided a reference for revealing the micro-milling mechanism of single crystal materials.

Size effects in the mechanical behavior of multilayer pile-ups embedded in channel microstructures are investigated in terms of work-hardening, plastic slip and geometrically necessary dislocations (GND) distributions. The mechanical responses with various channel sizes are computed by three-dimensional discrete dislocation dynamics (DDD), micromorphic crystal plasticity (Microcurl) and field dislocation mechanics (FDM). The analysis is first limited to single slip with a slip plane perpendicular to the channel walls. In DDD simulations, it is found that the overall work-hardening is strongly dependent on distance between neighbor slip layers. The size dependence disappears when the neighbor layers are close enough to interact with each other. It is confirmed by direct comparison between DDD simulations and two analytical expressions derived from simplified model of multilayer pile-ups. Distributions of slip and GNDs are presented and analyzed for various channel sizes. The cases of inclined slip plane and of double slip systems in a channel are also considered and investigated. The two alternative crystal plasticity theories, Microcurl and FDM, are then found to reproduce the results of DDD. In particular, quantitative correspondence is found between the Microcurl and DDD results.

A tool to implement a length scale dependency to classical crystal plasticity simulations is presented. Classical crystal plasticity models do not include a size effect; therefore, the size of the grain does not influence the simulated deformation. Classical crystal plasticity advancements have been through the inclusion of stress or strain gradient based constitutive models to improve the simulation of length scale dependent deformation. However, this tool presents an alternative to implementing a length scale, where the influence of slip pile-up in the form of dislocations at grain boundaries as a potential to explaining the Hall-Petch effect in materials. This is achieved by calculating the slip distance in adjacent grains for each slip system, by assuming the total slip length spans the grain in the slip direction. These calculations can occur in two ways. The first is the analysis occurs at the start of the simulation, therefore, only occurs once. If this approach is used, the computational cost of this tool is minute. However, if the simulations consider large deformations, during which it is expected that the grains are going to undergo large rotations, then it would be advantageous to the have the tool recalculate the information during the analysis. Consequently, the computational cost would depend on the resolution of the modelled geometry, the number of grains, and the number of slip systems. The tool also provides a capability to develop constitutive models based on complex grain boundary features which can be implemented in classical crystal plasticity models and gradient based crystal plasticity models. The described calculation process is implemented through a Fortran subroutine, which has been designed to be easily used in crystal plasticity simulations. The presented tool also includes Python code designed to link with microstructures built using DREAM.3D to extract the required input data to the Fortran subroutine.The proposed tool is not limited to classical crystal plasticity formulations, instead the data extracted and outputted from the Fortran subroutine can be used to serve alternative purposes in both stress and strain gradient crystal plasticity models.The proposed tool can be modified to extract additional data to that presented.The slip distance in the adjacent grain, the distance from the grain boundary of the current calculation point, and the interaction between slip systems between grains can be used in any crystal plasticity constitutive models.

Chapter 8 - Single-Arm Dislocation Source (SAS)-Controlled Submicron Plasticity

Micromechanical modeling of damage evolution and fracture behavior in particle reinforced metal matrix composites based on the conventional theory of mechanism-based strain gradient plasticity

Corrigendum to “Interpretation of the size effects in micropillar compression by a strain gradient crystal plasticity theory” [Int. J. Plast. 116 (2019) 280–296

Size effects on void growth in single crystals with distributed voids

Phase-field model and computational procedure during static primary recrystallization are developed. The developed procedure consists of following three steps. First, the microstructures of plastically deformed polycrystalline metal are simulated by finite element method based on strain gradient crystal plasticity theory. Second, the results such as the accumulated dislocation density and crystal orientation are mapped onto the regular lattices used in phase-field simulation. The stored energy that act as driving force of the grain boundary migration is calculated from the dislocation density and is smoothed to avoid the computational difficulty. Furthermore, the misorientation required for nucleation criteria is calculated on all lattices. Third, phase-field simulation during static primary recrystallization is performed by using mapped data. By conducting a series of numerical simulations, it has been confirmed that the recrystallization microstructure based on the deformation microstructure can be reproduced.

In this study, a crystal plasticity finite element method (CPFEM) model has been developed to investigate the anisotropic plastic behavior of (001) aluminum single crystal during high-pressure torsion (HPT). The distributions of equivalent plastic strain and Mises stress recorded on the sample surface are presented. The directional variations of plastic strain and Mises stress with the development of four-fold symmetry pattern are observed along the sample circumference. The crystallographic orientation evolution along the tangential direction is studied, and the corresponding lattice rotation and slip trace are predicted, respectively. The plastic anisotropy mechanism is discussed in detail based on the theory of crystal plasticity. The simulation results reveal that the differences in slip systems activation (dominant slip and multiple slips) are responsible for the anisotropic plastic deformation in HPT.